Free Algebra Tutorials! Home Systems of Linear Equations and Problem Solving Solving Quadratic Equations Solve Absolute Value Inequalities Solving Quadratic Equations Solving Quadratic Inequalities Solving Systems of Equations Row Reduction Solving Systems of Linear Equations by Graphing Solving Quadratic Equations Solving Systems of Linear Equations Solving Linear Equations - Part II Solving Equations I Summative Assessment of Problem-solving and Skills Outcomes Math-Problem Solving:Long Division Face Solving Linear Equations Systems of Linear Equations in Two Variables Solving a System of Linear Equations by Graphing Ti-89 Solving Simultaneous Equations Systems of Linear Equations in Three Variables and Matrix Operations Solving Rational Equations Solving Quadratic Equations by Factoring Solving Quadratic Equations Solving Systems of Linear Equations Systems of Equations in Two Variables Solving Quadratic Equations Solving Exponential and Logarithmic Equations Solving Systems of Linear Equations Solving Quadratic Equations Math Logic & Problem Solving Honors Solving Quadratic Equations by Factoring Solving Literal Equations and Formulas Solving Quadratic Equations by Completing the Square Solving Exponential and Logarithmic Equations Solving Equations with Fractions Solving Equations Solving Linear Equations Solving Linear Equations in One Variable Solving Linear Equations SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA SOLVING LINEAR EQUATIONS

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Solving Quadratic Equations by Factoring

Questions

1. Solve x2 − x − 20 = 0.
2. Solve x2 + 11x + 18 = 0.
3. Solve 8x2 = 72.
4. Solve (x − 5)(x + 4) = 2(x − 5).
5. Solve 6. Solve 7. The area of a rectangular garden is 140 square meters. The width is 3 meters longer than one-half of the length. Find
the length and width of the garden.

8. Jules is standing on a platform 6 meters high and throws a ball straight up as high as he can at a velocity of 13 meters
per second. At what time t will the ball hit the ground? How far from the ground is the ball 2 seconds after Jules threw
the ball (assume the ball is 6 meters from the ground when it leaves Jules’ hand).

Solutions

1.

 x2 − x − 20 = 0 Find two numbers product is −20 and sum is −1: −5, 4. (x − 5)(x + 4) = 0 Use Zero Factor Property. (x − 5) = 0 or (x + 4) = 0 Solve each linear equation. x = 5 or x = −4

Check:
(5)2 − (5) − 20 = 25 − 25 = 0
(−4)2 − (−4) − 20 = 16 − 16 = 0

2.

 x2 + 11x + 18 = 0 Find two numbers product is 18 and sum is 11: 2, 9. (x + 2)(x + 9) = 0 (x + 2) = 0 or (x + 9) = 0 x = −2 or x = −9

Check:
(−2)2 + 11(−2) + 18 = 4 − 22 + 18 = 0
(−9)2 + 11(−9) + 18 = 81 − 99 + 18 = 0

3.

 8x2 − 72 = 0 Factor. 8(x2 − 9) = 0 Factor. x2 − 9 = 0 Divide by 8. Difference of Squares. (x + 3)(x − 3) = 0 (x + 3) = 0 or (x − 3) = 0 x = −3 or x = 3

Check:
8(−3)2 = 8(9) = 72
8(3)2 = 8(9) = 72

Alternate solution, which only works because there was no x term:

 8x2 = 72 x2 = 9 when taking square root of both sides of equation, one side can be ±. x = ±3

4. Start by multiplying everything to get in form ax2 + bx + c = 0.

(x − 5)(x + 4) = 2(x − 5)
x2 − x − 20 = 2x − 10
x2 − x − 20 − 2x + 10 = 0
x2 − 3x − 10 = 0 Find two numbers product is −10 and sum is −3: −5, 2.
(x − 5)(x + 2) = 0
(x − 5) = 0 or (x + 2) = 0
x = 5 or x = −2

Check:
((5) − 5)((5) + 4) − 2((5) − 5) = 0
((−2) − 5)((−2) + 4) − 2((−2) − 5) = −14 + 14 = 0

5. Start by multiplying everything to get in form ax2 + bx + c = 0. x2 + 5x = 24
x2 + 5x − 24 = 0 Find two numbers product is −24 and sum is 5: 8,−3.
(x + 8)(x − 3) = 0
(x + 8) = 0 or (x − 3) = 0
x = −8 or x = 3

Check: 6. Start by multiplying everything to get in form ax2 + bx + c = 0.  Grouping Method: Find two numbers product is −30 and sum is −1: −6, 5. Factor by grouping. Check: 7. Let x be the length (in meters). Then the width is x/2 + 3 meters. Area is 140 m2.

Area = (length)(width)  write in form ax2 + bx + c = 0. x2 + 6x − 280 = 0 Find two numbers product is 6 and sum is −280: −14, 20.
(x − 14)(x + 20) = 0
(x − 14) = 0 or (x + 20) = 0
x = 14 or x = −20

Exclude the x = −20 as unphysical (can’t have negative length). So The length is x = 14 meters. Width is 10 meters.

8. Set h = 6 and v = 13 in our model equation S = −5t2 + vt + h (see handout).

5t2 + 13t + 6 = 0 Ball hits ground when S = 0. Use Grouping Method to factor.
−5t2 + 13t + 6 = 0 Find two numbers product is −30 and sum is 13: 15,−2.
−5t2 + 15t − 2t + 6 = 0
−5t(t − 3) − 2(t − 3) = 0
(−5t − 2)(t − 3) = 0
(−5t − 2) = 0 or (t − 3) = 0
t = −2/5 or t = 3

Exclude the t = −5/3 as unphysical, so the ball hits the ground after 3 seconds.

Two second after throwing the ball, it it S = −5(2)2 + 13(2) + 6 = −20 + 26 + 6 = 12 meters above the ground.